The radius of the orbit of a geostationary satellite is (mean radius of earth is ' R ', angular velocity about own axis is ' ω ' and acceleration due to gravity on earth's surface is ' g ') (a) ((gR²)/(ω²))1/3 (b) ((gR²)/(ω²))2/3 (c) ((gR²)/(ω²))1/2 (d) (gR²)/(ω²)

Answer: (a). Geostationary orbit: GM/r² = ω² r ⇒ r³ = (GM)/(ω²). Use GM = gR²: r³ = (gR²)/(ω²). r = ((gR²)/(ω²))1/3 So the answer is (a).

The radius of the orbit of a geostationary satellite is (mean radius… | MHT CET 2023 (11 May, Shift 2)

Q33MHT CET 2023 · 11 MAY · SHIFT 2Easy

Satellites - Orbital Velocity & Period

The radius of the orbit of a geostationary satellite is (mean radius of earth is ' $R$ ', angular velocity about own axis is ' $\omega$ ' and acceleration due to gravity on earth's surface is ' $g$ ')

Show answer and solution

Answer: (a)

Geostationary orbit: $\frac{GM}{r^2} = \omega^2 r \Rightarrow r^3 = \frac{GM}{\omega^2}$ .
Use $GM = gR^2$ : $r^3 = \frac{gR^2}{\omega^2}$ .
$r = \left(\frac{gR^2}{\omega^2}\right)^{1/3}$
So the answer is (a).

Report a mistake

Satellites - Orbital Velocity & Period question from MHT CET 2023 (11 May, Shift 2)

More questions on Satellites - Orbital Velocity & Period